1. Field of the Invention:
The present invention relates to magnetic resonance imaging (MRI) techniques and, more particularly, to a technique for recovering MRI signals resulting from the application of time varying gradients.
2. Description of the Related Art:
Primary among the factors currently limiting the rate of growth of MRI in the diagnostic imaging marketplace are concerns relating to its limited applicability to the study of organ systems subject to significant involuntary physiological motion, especially of the heart. This problem can be alleviated by decreasing data acquisition time. By reducing the total scan time to a small fraction of the cardiac period, motion artifacts due to all physiological motions including that of the heart, are avoided.
In an effort to reduce data acquisition time, MRI methods using time-varying gradients have been developed. See, for example, U.S. Pat. No. 4,740,748. In this patent, orthogonal sinusoidal gradient fields are modulated during the observation of a free induction decay (FID) signal to scan the spatial frequency domain (hereinafter referred to as "k-space") and efficiently collect the data necessary for image reconstruction. Since data acquisition occurs during a single FID, imaging occurs in less than 100 milliseconds, thus overcoming problems such as motion artifacts discussed above.
The actual MRI image is generated by performing a two-dimensional Fourier transform of the data acquired from the transversal through k-space effected by the time-varying gradients However, if the sampling of k-space is to be linear, the data acquired must necessarily be sampled non-linearly because of the time-variance of the gradients. In order to obtain linear data, non-linear sampling techniques can be employed, but such sampling is quite difficult to implement and must be modified wherever the waveform of the gradient is changed.
As an alternative, researchers have turned reconstruction techniques which employ postfiltering of observed FID signals. See, e.g., A. Maeda, "Reconstruction by Weighted Correlation for MRI with Time-Varying Gradients", IEEE Transactions of Medical Imaging, Vol 7, No. 1 pp. 26-31 (March 1988). The technique disclosed in this paper estimates spin density by calculating the "weighted" correlation of the observed FID signal and the phase modulation function at each point.
The present invention is similarly directed to a technique for reconstructing images by appropriate filtering of data acquired during linear sampling of k-space. Accordingly, the primary object of the present invention is to provide an optimum filter for processing MRI signals resulting from time varying gradients, specifically sinusoidal gradients.